The abundance of O in planetary nebulae (PNe) has been historically used as a metallicity indicator of the interstellar medium (ISM), where they originated; e.g. it has been widely used to study metallicity gradients in our Galaxy and beyond. However, clear observational evidence for O self-enrichment in low-metallicity Galactic PNe with C-rich dust has been recently reported. Here, we report asymptotic giant branch (AGB) nucleosynthesis predictions for the abundances of the CNO elements and helium in the metallicity range Z⊙/4 < Z < 2 Z⊙. Our AGB models, with diffusive overshooting from all the convective borders, predict that O is overproduced in low-Z low-mass (˜1-3 M⊙) AGB stars and nicely reproduce the recent O overabundances observed in C-rich dust PNe. This confirms that O is not always a good proxy of the original ISM metallicity and other chemical elements such as Cl or Ar should be used instead. The production of oxygen by low-mass stars should be thus considered in galactic-evolution models.